Recent advances in the study of dynamical systems have revolutionized the way that classical mechanics is taught and understood. This new and comprehensive textbook provides a complete description of this fundamental branch of physics. The authors cover all the material that one would expect to find in a standard graduate course: Lagrangian and Hamiltonian dynamics, canonical transformations, the Hamilton-Jacobi equation, perturbation methods, and rigid bodies. They also deal with more advanced topics such as the relativistic Kepler problem, Liouville and Darboux theorems, and inverse and chaotic scattering. A key feature of the book is the early introduction of geometric (differential manifold) ideas, as well as detailed treatment of topics in nonlinear dynamics (such as the KAM theorem) and continuum dynamics (including solitons). Over 200 homework exercises are included. It will be an ideal textbook for graduate students of physics, applied mathematics, theoretical chemistry, and engineering, as well as a useful reference for researchers in these fields. A solutions manual is available exclusively for instructors.
One of the best and most complete textbooks I've ever come across for Classical Mechanics. It's outrageous to even think of using Goldstein's book, when you have a golden standard like this one for Advanced Undergraduate and Graduate courses.
What this book does best is that it provides the reader with excellent geometrical insight, which helps develop a real intuition for the subject and also spot what's missing. This helps while dealing with theories like Relativity and Non Linearity, to which this textbook also provides excellent introductions.